A: If you plan to shut-down your water garden, you should drain the water down below the skimmer opening and yes you would leave the water in the pond. The reason for this is to help prevent some shifting within the water garden. The ground will shift throughout the winter and if you were to drain the water garden entirely, it could cause certain sections of the water garden to cave in. Having the water in there will keep everything at bay by applying pressure to all sides.
Also, when lowering the water level below the skimmer, make sure to drain the skimmer out entirely. Allowing the water in the skimmer to freeze could cause damage to the skimmer itself. The same goes for the waterfall filter. As for what to do with the pump, here is a link to a previous post.